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Mathematical Charts and Tables

Special Purpose Tables

Special Purpose Tables

From at least the 1930s through the 1960s, American manufacturers distributed a variety of tables that customers might use. This was sometimes in the form of a pamphlet, such as the set of miscellaneous hydraulic tables for designers prepared by the Southwark Foundry and Machine Company Division of Baldwin-Southwark Corporation in 1931. Other special purpose tables, distributed on slide charts of various sorts, described properties of such materials as leaded bronze, nickel alloys, specialty steels, wire cloth, glass, and salt/water mixtures. Others gave properties of compressors, elements of screw threads, and data on the dietary advantages of various forms of meat, The Aetna insurance company prepared a table instructing drivers on the safe distances to be maintained between cars. As late as 1969, a manufacturer of paper goods distributed a slide chart for calculating the cost per ounce of groceries, and urged consumers to make careful comparisons of prices. Some tables were not associated with any specific product. Thus the “Menu Minder,” distributed in the mid-1970s, allowed one to quickly alter recipes to serve more or fewer people. It may have been distributed as a kitchen novelty by any number of firms.

Tables distributed by business machine manufacturers have been mentioned already. In addition to covering the needs of commerce and special forms of manufacturing, some of these offered ways to estimate square roots and cube roots.

Specialized tables also were prepared for government use. Military contractors prepared tables to assist in aiming guns and filling out Air Force inventory forms. The Atomic Energy Commission prepared a table for use in uranium enrichment plants.

This orange and black paper device has a set of tables printed on both sides of a piece of cardboard that slides between two other pieces of cardboard that are riveted together. The whole thing fits in a cardboard envelope. The tables are used to calculate the total heat gain from light shining through windows and other glass in a building. The instrument was distributed by Libbey Owens Ford Company, a glass firm in Ohio.

A mark on the envelope and the object reads: HEAT GAIN CALCULATOR; A paper sticker attached to the envelope reads: Display Copy Only (/) Please do not remove. A mark on the back of the instrument in the bottom right corner reads: ... 1975, PERRYGRAF Div., Nashua LA. CA 90064 Printed in U.S.A. A mark on the front left corner reads: LOF (/) GLASS (/) 811 MADISON AVENUE (/) TOLEDO, OHIO 43695. A mark on the front of the instrument reads: LIBBEY (/) OWENS (/) FORD (/) COMPANY.

This red, white, and blue cardboard slide chart has logarithmic scales for calculating the cost per ounce or unit of goods selling at prices ranging from ten cents to ten dollars apiece. The cost is given on the envelope, the number of ounces or units on the sliding scale, and the cost per ounce or unit on a scale below on the slide. Windows in the envelope reveal the scales.

The reverse side of the slide has a listing of the calorie content of a single serving of selected common foods and beverages.

This rotating cylindrical table helps a cook to alter the quantities of ingredients in recipes.

A three-column table on the left side indicates how quantities should be multiplied for a recipe with four servings to one with six or eight servings. The rightmost column (for four servings) has the numbers 1, 1-1/3, 2, 3, 6, 8, 10, and 12, with the numbers in the middle column ranging from 1 1/2 to 18 and the numbers in the third column from 2 to 24.

A second table show how one should alter the number of cups, tablespoons and teaspoons in a recipe to change it by a factor of 3, 2, 3/4, 1/2, 1/4, 2/3, or 1/3. The cylinder has knobs at both ends for rotation. It is enclosed in a brown plastic case with a clear plastic front that has a sticker attached to it. Two windows in the sticker show the tables.

A mark on the center of the sticker reads: MENU MINDER (/) A RECIPE CALCULATOR. A mark on its right edge reads; COPYRIGHT WILLE ENTERPRISES 1974. A mark on the back reads: MFG BY (/) PROTO PRODUCTION PLAS [. . .] (/) BOULDER COLO. The mark on the back is partly obscured by two of five magnets that will hold the Menu Minder to a metal surface.

Before the introduction of calculating machines that could compute cube roots of numbers directly, calculating machine manufacturers distributed tables to assist in these calculations. This table was developed by employees of Marchant Calculating Machine Company in Oakland, California, for use with its machines.

The table is of heavy paper, printed in black., and includes instructions on how it is to be used to find cube roots to the fifth and to the tenth significant figure. A drawing of a Marchant calculating machine is at the top, toward the left. A mark at the bottom left reads: TABLE 68. Another mark along the bottom reads: PRINTED IN U. S. A. A third mark along the bottom reads: COPYRIGHT 1944 MARCHANT CALCULATING MACHINE COMPANY, OAKLAND, CALIF., U. S. A.

The table is based on the observation that if three numbers are almost the same size, then their arithmetic mean (the average value of the three numbers) is nearly equal to their geometric mean (the cube root of the product of the numbers). Suppose three such numbers are A, A, and N (the first two numbers are the same). Then the the cube root of the expression N times A squared equals (N+2A)/3, or the cube root of N equals (N+ 2A) / (3 (A)2/3). The table gives values of A and three times A to the 2/3, for A running from 100 to 999. A user can compute the cube root of a number N by finding the A nearest N, adding N and twice A, and dividing the sum (using a calculating machine) by three times A to the two thirds power, as given in the table. The instructions suggest how the procedure should be modified according to the decimal value of the number.

Compare 313984.03, which gives a table for finding square roots. The table came with Marchant calculating machine MA*334384. The donor, Richard H. Hronik (1911–2003), held a number of patents in transportation engineering and did design work relating to railroad systems built for the Indian government. He went on to work for the firm Melpar as a materials science engineer.

Before the introduction of calculating machines that could compute cube roots of numbers directly, calculating machine manufacturers distributed tables to assist in these calculations. This table was developed by employees of Marchant Calculating Machine Company in Oakland, California, for use with its machines.

The table is of heavy paper, printed in black. and includes instructions on how it is to be used to find cube roots to the fifth and to the tenth significant figure. A drawing of a Marchant calculating machine is at the top toward the left. A mark at the bottom left reads: TABLE 68. Another mark along the bottom reads: PRINTED IN U. S. A. A third mark along the bottom reads: COPYRIGHT 1944 MARCHANT CALCULATING MACHINE COMPANY, OAKLAND, CALIF., U. S. A.

The table is based on the observation that if three numbers are almost the same size, then their arithmetic mean (the average value of the three numbers) is nearly equal to their geometric mean (the cube root of the product of the numbers). Suppose three such numbers are A, A, and N (the first two numbers are the same). Then the the cube root of the expression N times A squared equals (N+2A)/3, or the cube root of N equals (N+ 2A) / (3 (A)2/3). The table gives values of A and three times A to the 2/3, for A running from 100 to 999. A user can compute the cube root of a number N by finding the A nearest N, adding N and twice A, and dividing the sum (using a calculating machine) by three times A to the two thirds power, as given in the table. The instructions suggest how the procedure should be modified according to the decimal value of the number.

Compare 313984.03, which gives a table for finding square roots. The table came with Marchant calculating machine MA*334384. The donor, Richard H. Hronik (1911–2003), held a number of patents in transportation engineering and did design work relating to railroad systems built for the Indian government. He went on to work for the firm of Melpar as a materials science engineer.

These two paper leaflets provide numerical values needed for finding square roots to eight significant digits (Table No. 80) and to six significant digits (Table No. 81). Table 80 was copyrighted in 1951, Table 81 in 1952. These copies of the tables were issued after Marchant became a division of Smith-Corona Marchant Inc. in 1958.

Table 80 allows one to compute square roots on a calculating machine to eight significant digits using a combination of additions and two divisions. Table 81 allows one to find less precise values of the same function using additions and only one division.

This chart has a black image marked on a rigid white plastic sheet. Five equally spaced concentric circles are divided into eight equal sections by lines through the center of the circle. The outermost circle is divided into 64 equal segments, which are numbered counterclockwise from 0 to 32 on the left half of the circle. On the right half, segments are numbered from 0 at the bottom counterclockwise to 30 at the top, and also from (34) to (64).

A mark at the bottom left reads: CARD, TANK RANGE (/) 8724207. A mark on the left top reads: HUNDREDS OF MILS. There are 6400 mils in a circle of 360 degrees angular measure.

The object comes from the Felsenthal Collection of computing devices. According to the accession file it was made by Felsenthal for the U.S. Army in 1955, and had Felsenthal designation FA0-51. It may have been used by the tank gunner to lay his gun on target, before the availability of electronic or laser sighting.

This device assists in calculations of changes in the range of a gun because of meteorological conditions, particularly wind speed and temperature. A rotating disc and pointer attached to the plastic base have the scales required to correct for wind speed. A scale toward the bottom of the base gives the temperature correction. Both of these corrections are in percentages of the range. Summing them gives the total meteorological correction as a percentage of the range. One then can use a range correction chart to find the actual range correction.

This white plastic chart was designed for the U.S. Army Signal Corps. It is a nomogram for finding the range correction in yards of a weapon, by lining up the meteorological correction as a percentage of the range and the range.

On the left is a scale marked “Range Correction in Yds.” On the right is a scale marked “Percentage Meteorological Correction” and on the diagonal between the two is a scale marked “Range in Yds.” According to a label received with the object and stored in the accession file, the object was made in 1945.

The meteorological correction is found from the temperature and wind speed using a related chart called a “sound velocity corrector” (for an example, see 1977.1141.42) .

A mark on the object reads: Range Correction Chart PT-63/TSS-1.

For an explanation of the mathematical theory of this kind of nomogram, see Lipka. For a similar device used for another purpose, see 1985.0636.01.

This slide chart is designed to assist in coding United States Air Force forms for inventory control. The envelope is of clear plastic printed in blue, with a white plastic card that slides crosswise. The sliding card has columns for eight Air Force forms (forms number 158A&B, 158C&D, 813, 814, 815, 158-7, 366J&K, and 366L&M). The numbers in each column indicate the place on the form on which the data is to be entered. For example, in all eight forms spaces 1through15 are for the stock number and spaces 31through 34 are for the organization number. The first 56 spaces are described on the front of the sliding card. The remainder (up to 80) are on the back.

It is possible that the forms described are 80-column punch cards, such as those made by IBM for use with electronic data processing equipment.

A mark on the front of the envelope reads: Code Designator (/) Slide Chart. A mark on the back of the envelope reads: Felsenthal Instruments Co.1963 (/) Chicago 31, Illinois (/) MFR’s PT.NO. FAA-141-A.